2022ApJ...927...84Z

It has been widely recognized that gamma-ray burst (GRB) afterglows arise from interactions between the GRB outflow and circumburst medium, while their evolution follows the behaviors of relativistic shock waves. Assuming the distribution of circumburst medium follows a general power-law form, that is, n = A _* R ^–k , where R denotes the distance from the burst, it is obvious that the value of the density-distribution index k can affect the behaviors of the afterglow. In this paper, we analyze the temporal and spectral behaviors of GRB radio afterglows with arbitrary k values. In the radio band, a standard GRB afterglow produced by a forward shock exhibits a late-time flux peak, and the relative peak fluxes, as well as peak times at different frequencies, show dependencies on k. Thus, with multiband radio-peak observations, one can determine the density profile of the circumburst medium by comparing the relations between peak flux/time and frequency at each observing band. Also, the effects of transrelativistic shock waves, as well as jets in afterglows, are discussed. By analyzing 31 long and 1 short GRB with multiband data of radio afterglows, we find that nearly half of them can be explained with a uniform interstellar medium (k = 0), ∼1/5 can be constrained to exhibiting a stellar-wind environment (k = 2), while less than ∼1/3 of the samples show 0 < k < 2.